Question

The average of 3 prime numbers lying between 47 and 74 is $\frac{191}{3}$. The greatest possible difference between any two out of the 3 prime numbers is:

• A. 12
• B. 14
• C. 18
• D. can't be determined

Answer 1

The correct option is C 18

There are 6 prime numbers between 47 and 74 as given below:
53, 59, 61, 67, 71, 73
There are only two combinations whose average is $\frac{191}{3}$ or whose total sum is 191.
These are, {53, 67, 71} and {59, 61, 71}
We observe that in the first set the difference between greatest and smallest prime number is 18.
Hence choice (c) is correct.